In certain situations like cross word puzzle it wasnt usual to use "umlaut" but instead to write oe, ue and ae. In Swiss German people dont use ß. So transcription was always a thing to know.

For German these rules are offical. They're used in the machine readable part of ID cards and passports. If you start at a german company and they setup an e-mail address for you they'll use these rules too. The origin of the letters ä, ö and ü in German are ae, oe and ue, people just put the e on top of the vowel and they slowly transformed into what we use today. You can still see this in some names like Goethe.

I know that, but it's not what I meant, but probably didn't make it clear enough.

Germans know these official rules and maybe linguists, but if you present the typical English speaker with Möller vs Moeller it's confusing. Look at the media (who could, maybe, do some research?) who write Jurgen and not Jürgen. That's my point, the official rules don't help if everyone ignores them, for whatever reason.

German has an official and fully information preserving transcription to basic latin (which is really what all this talk about "anglo letters" is, just the basic latin letters in common use in the early modern era, with no diacritics at all), which can be used in official documents, too. Other languages, like latinized Turkish, obviously copied the diacritics, but seem to have left out the transcription rules, most probably because they borrowed the letters long after their history was relevant.